Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRN |
Texto Completo: | https://repositorio.ufrn.br/handle/123456789/30327 |
Resumo: | Conformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limited to situations in which the bulk is uniform because CFT describes low-energy excitations around some energy scale, taken to be constant throughout the system. However, in many experimental contexts, such as quantum gases in trapping potentials and in several out-of-equilibrium situations, systems are strongly inhomogeneous. We show here that the powerful CFT methods can be extended to deal with such 1D situations, providing a few concrete examples for non-interacting Fermi gases. The system’s inhomogeneity enters the field theory action through parameters that vary with position; in particular, the metric itself varies, resulting in a CFT in curved space. This approach allows us to derive exact formulas for entanglement entropies which were not known by other means |
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Dubail, JérômeStéphan, Jean-MarieViti, JacopoCalabrese, Pasquale2020-10-08T22:02:32Z2020-10-08T22:02:32Z2017-02-13DUBAIL, Jerome; STÉPHAN, Jean-Marie; VITI, Jacopo; CALABRESE, Pasquale. Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting fermi gases. Scipost Physics, [S.L.], v. 2, n. 1, p. 1-22, 13 fev. 2017. Disponível em: https://scipost.org/10.21468/SciPostPhys.2.1.002. Acesso em: 18 ago. 2020. http://dx.doi.org/10.21468/scipostphys.2.1.0022542-4653https://repositorio.ufrn.br/handle/123456789/3032710.21468/SciPostPhys.2.1.002Stichting SciPostAttribution 3.0 Brazilhttp://creativecommons.org/licenses/by/3.0/br/info:eu-repo/semantics/openAccessField theoryOne-dimensionalquantum systemsInhomogeneous quantum systemsConformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gasesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleConformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limited to situations in which the bulk is uniform because CFT describes low-energy excitations around some energy scale, taken to be constant throughout the system. However, in many experimental contexts, such as quantum gases in trapping potentials and in several out-of-equilibrium situations, systems are strongly inhomogeneous. We show here that the powerful CFT methods can be extended to deal with such 1D situations, providing a few concrete examples for non-interacting Fermi gases. The system’s inhomogeneity enters the field theory action through parameters that vary with position; in particular, the metric itself varies, resulting in a CFT in curved space. This approach allows us to derive exact formulas for entanglement entropies which were not known by other meansengreponame:Repositório Institucional da UFRNinstname:Universidade Federal do Rio Grande do Norte (UFRN)instacron:UFRNORIGINALConformalFieldTheory_VITI_2017.pdfConformalFieldTheory_VITI_2017.pdfapplication/pdf1692782https://repositorio.ufrn.br/bitstream/123456789/30327/1/ConformalFieldTheory_VITI_2017.pdfbb77444e2d61cc26c5bee84d83f864c1MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8914https://repositorio.ufrn.br/bitstream/123456789/30327/2/license_rdf4d2950bda3d176f570a9f8b328dfbbefMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81484https://repositorio.ufrn.br/bitstream/123456789/30327/3/license.txte9597aa2854d128fd968be5edc8a28d9MD53TEXTConformalFieldTheory_VITI_2017.pdf.txtConformalFieldTheory_VITI_2017.pdf.txtExtracted texttext/plain57180https://repositorio.ufrn.br/bitstream/123456789/30327/4/ConformalFieldTheory_VITI_2017.pdf.txt07ec63cf489022f105eb0cad229045efMD54THUMBNAILConformalFieldTheory_VITI_2017.pdf.jpgConformalFieldTheory_VITI_2017.pdf.jpgGenerated Thumbnailimage/jpeg1600https://repositorio.ufrn.br/bitstream/123456789/30327/5/ConformalFieldTheory_VITI_2017.pdf.jpg44555db3490471e68d95d96288b8c824MD55123456789/303272020-10-11 04:38:21.462oai:https://repositorio.ufrn.br:123456789/30327Tk9OLUVYQ0xVU0lWRSBESVNUUklCVVRJT04gTElDRU5TRQoKCkJ5IHNpZ25pbmcgYW5kIGRlbGl2ZXJpbmcgdGhpcyBsaWNlbnNlLCBNci4gKGF1dGhvciBvciBjb3B5cmlnaHQgaG9sZGVyKToKCgphKSBHcmFudHMgdGhlIFVuaXZlcnNpZGFkZSBGZWRlcmFsIFJpbyBHcmFuZGUgZG8gTm9ydGUgdGhlIG5vbi1leGNsdXNpdmUgcmlnaHQgb2YKcmVwcm9kdWNlLCBjb252ZXJ0IChhcyBkZWZpbmVkIGJlbG93KSwgY29tbXVuaWNhdGUgYW5kIC8gb3IKZGlzdHJpYnV0ZSB0aGUgZGVsaXZlcmVkIGRvY3VtZW50IChpbmNsdWRpbmcgYWJzdHJhY3QgLyBhYnN0cmFjdCkgaW4KZGlnaXRhbCBvciBwcmludGVkIGZvcm1hdCBhbmQgaW4gYW55IG1lZGl1bS4KCmIpIERlY2xhcmVzIHRoYXQgdGhlIGRvY3VtZW50IHN1Ym1pdHRlZCBpcyBpdHMgb3JpZ2luYWwgd29yaywgYW5kIHRoYXQKeW91IGhhdmUgdGhlIHJpZ2h0IHRvIGdyYW50IHRoZSByaWdodHMgY29udGFpbmVkIGluIHRoaXMgbGljZW5zZS4gRGVjbGFyZXMKdGhhdCB0aGUgZGVsaXZlcnkgb2YgdGhlIGRvY3VtZW50IGRvZXMgbm90IGluZnJpbmdlLCBhcyBmYXIgYXMgaXQgaXMKdGhlIHJpZ2h0cyBvZiBhbnkgb3RoZXIgcGVyc29uIG9yIGVudGl0eS4KCmMpIElmIHRoZSBkb2N1bWVudCBkZWxpdmVyZWQgY29udGFpbnMgbWF0ZXJpYWwgd2hpY2ggZG9lcyBub3QKcmlnaHRzLCBkZWNsYXJlcyB0aGF0IGl0IGhhcyBvYnRhaW5lZCBhdXRob3JpemF0aW9uIGZyb20gdGhlIGhvbGRlciBvZiB0aGUKY29weXJpZ2h0IHRvIGdyYW50IHRoZSBVbml2ZXJzaWRhZGUgRmVkZXJhbCBkbyBSaW8gR3JhbmRlIGRvIE5vcnRlIHRoZSByaWdodHMgcmVxdWlyZWQgYnkgdGhpcyBsaWNlbnNlLCBhbmQgdGhhdCB0aGlzIG1hdGVyaWFsIHdob3NlIHJpZ2h0cyBhcmUgb2YKdGhpcmQgcGFydGllcyBpcyBjbGVhcmx5IGlkZW50aWZpZWQgYW5kIHJlY29nbml6ZWQgaW4gdGhlIHRleHQgb3IKY29udGVudCBvZiB0aGUgZG9jdW1lbnQgZGVsaXZlcmVkLgoKSWYgdGhlIGRvY3VtZW50IHN1Ym1pdHRlZCBpcyBiYXNlZCBvbiBmdW5kZWQgb3Igc3VwcG9ydGVkIHdvcmsKYnkgYW5vdGhlciBpbnN0aXR1dGlvbiBvdGhlciB0aGFuIHRoZSBVbml2ZXJzaWRhZGUgRmVkZXJhbCBkbyBSaW8gR3JhbmRlIGRvIE5vcnRlLCBkZWNsYXJlcyB0aGF0IGl0IGhhcyBmdWxmaWxsZWQgYW55IG9ibGlnYXRpb25zIHJlcXVpcmVkIGJ5IHRoZSByZXNwZWN0aXZlIGFncmVlbWVudCBvciBhZ3JlZW1lbnQuCgpUaGUgVW5pdmVyc2lkYWRlIEZlZGVyYWwgZG8gUmlvIEdyYW5kZSBkbyBOb3J0ZSB3aWxsIGNsZWFybHkgaWRlbnRpZnkgaXRzIG5hbWUgKHMpIGFzIHRoZSBhdXRob3IgKHMpIG9yIGhvbGRlciAocykgb2YgdGhlIGRvY3VtZW50J3MgcmlnaHRzCmRlbGl2ZXJlZCwgYW5kIHdpbGwgbm90IG1ha2UgYW55IGNoYW5nZXMsIG90aGVyIHRoYW4gdGhvc2UgcGVybWl0dGVkIGJ5CnRoaXMgbGljZW5zZQo=Repositório de PublicaçõesPUBhttp://repositorio.ufrn.br/oai/opendoar:2020-10-11T07:38:21Repositório Institucional da UFRN - Universidade Federal do Rio Grande do Norte (UFRN)false |
dc.title.pt_BR.fl_str_mv |
Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases |
title |
Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases |
spellingShingle |
Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases Dubail, Jérôme Field theory One-dimensionalquantum systems Inhomogeneous quantum systems |
title_short |
Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases |
title_full |
Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases |
title_fullStr |
Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases |
title_full_unstemmed |
Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases |
title_sort |
Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases |
author |
Dubail, Jérôme |
author_facet |
Dubail, Jérôme Stéphan, Jean-Marie Viti, Jacopo Calabrese, Pasquale |
author_role |
author |
author2 |
Stéphan, Jean-Marie Viti, Jacopo Calabrese, Pasquale |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Dubail, Jérôme Stéphan, Jean-Marie Viti, Jacopo Calabrese, Pasquale |
dc.subject.por.fl_str_mv |
Field theory One-dimensionalquantum systems Inhomogeneous quantum systems |
topic |
Field theory One-dimensionalquantum systems Inhomogeneous quantum systems |
description |
Conformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limited to situations in which the bulk is uniform because CFT describes low-energy excitations around some energy scale, taken to be constant throughout the system. However, in many experimental contexts, such as quantum gases in trapping potentials and in several out-of-equilibrium situations, systems are strongly inhomogeneous. We show here that the powerful CFT methods can be extended to deal with such 1D situations, providing a few concrete examples for non-interacting Fermi gases. The system’s inhomogeneity enters the field theory action through parameters that vary with position; in particular, the metric itself varies, resulting in a CFT in curved space. This approach allows us to derive exact formulas for entanglement entropies which were not known by other means |
publishDate |
2017 |
dc.date.issued.fl_str_mv |
2017-02-13 |
dc.date.accessioned.fl_str_mv |
2020-10-08T22:02:32Z |
dc.date.available.fl_str_mv |
2020-10-08T22:02:32Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
DUBAIL, Jerome; STÉPHAN, Jean-Marie; VITI, Jacopo; CALABRESE, Pasquale. Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting fermi gases. Scipost Physics, [S.L.], v. 2, n. 1, p. 1-22, 13 fev. 2017. Disponível em: https://scipost.org/10.21468/SciPostPhys.2.1.002. Acesso em: 18 ago. 2020. http://dx.doi.org/10.21468/scipostphys.2.1.002 |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufrn.br/handle/123456789/30327 |
dc.identifier.issn.none.fl_str_mv |
2542-4653 |
dc.identifier.doi.none.fl_str_mv |
10.21468/SciPostPhys.2.1.002 |
identifier_str_mv |
DUBAIL, Jerome; STÉPHAN, Jean-Marie; VITI, Jacopo; CALABRESE, Pasquale. Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting fermi gases. Scipost Physics, [S.L.], v. 2, n. 1, p. 1-22, 13 fev. 2017. Disponível em: https://scipost.org/10.21468/SciPostPhys.2.1.002. Acesso em: 18 ago. 2020. http://dx.doi.org/10.21468/scipostphys.2.1.002 2542-4653 10.21468/SciPostPhys.2.1.002 |
url |
https://repositorio.ufrn.br/handle/123456789/30327 |
dc.language.iso.fl_str_mv |
eng |
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eng |
dc.rights.driver.fl_str_mv |
Attribution 3.0 Brazil http://creativecommons.org/licenses/by/3.0/br/ info:eu-repo/semantics/openAccess |
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Attribution 3.0 Brazil http://creativecommons.org/licenses/by/3.0/br/ |
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openAccess |
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Stichting SciPost |
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Stichting SciPost |
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